Ball piston hydrostatic machines

ABSTRACT

A ball piston hydrostatic machine comprises a cylinder block in which are formed a plurality of cylinders at a constant pitch. Ball pistons working within the cylinders run on a cam track defining the stroke of each ball piston in its cylinder and having fewer complete cam lobes lying between the points of contact of the first and last balls with the cam than the total number of balls multiplied by the ball pitch. Each cam lobe is so profiled as to produce a ball stroke including a period of constant acceleration and a period of constant deceleration with or without an intermediate period of constant velocity. The duration of the latter, as a proportion of the total ball stroke, is predetermined by the number (n) of ball pistons and the number (m) of cam lobes according to the expression:

United States Patent Donald Firth;

[Ill 3,561,329

[72] Inventors 2,617,360 11/1952 Barker 103/162 Sinclair Cunning am, g2,882,831 4/1959 Dannevig 103/161 Scotland 3,046,950 7/1962 Smith103/174 [21] A pl No. 871,750 3,151,529 10/1964 Leath 91/205 [22] FiledOct. 28, 1969 3,287,993 1 H1966 Lommicki 103/174 [45] Patented Feb 9,1971 I t FOREIGN PATENTS [731 Asslgnee ggifig m 906,553 9/1962 GreatBritain 103/161 London, England Primary ExaminerWilliam L. F reeh [32]Priority Aug. 15, 1964, Nov. 20, 1964,July 31, Attorney- Larson, Taylor& Hinds 1965 G' tBritain 51 47458/64 and 32362/65 ABSTRACT: A ballpiston hydrostatic machine comprises a Communion of application s N0.cylinder block in which are formed a plurality of cylinders at a 711966Man 11, 1968, now abandoned constant pitch. Ball pistons working Withinthe cylinders run on a cam track defining the stroke of each ball pistonin its cylinder and having fewer complete cam lobes lying between [54]BALL PISTON HYDROSTATIC MACHINES the points of contact of the first andlast balls with the cam 7 Claims, 17 Drawing Figs. than the total numberof balls multiplied by the ball pitch. Each cam lobe is so rofiled as toreduce a ball stroke includ- 9 498; P P [52] US. Cl 412/2 73 g a periodf constant acceleration and a period of constant 51 I t Cl F04b 27/00deceleration with or without an intermediate period of conl n F04b27/08, mm Velocity. The duration ofthe latter, as a proportion Ofthe 50M Search 103N161 total ball stroke, is predetermined by the number (n)of ball 1 1e 0 162 91/205 pistons and the number (m) of cam lobesaccording to the expression: l 2l(x)/n [56] References Cited here UNlTEDSTATE PATENTS l= the highest common factor of m and n, and 2,101,82912/1937 Benedek 103/161 x= an integer 31 n/2l and is even when n/l iseven.

52 J4 T n 1 F! +4, A 55 7 349 f'i rflfi w F' rb 2 fie-M 11* a! 1 5H 1 II I Q Q PATENIED FEB 9 I97! SHEET 5 0F 8 PATENTED FEB 9m 3561.329 SHEET5 BF 8 PATENTEU FEB 91am SHEET 7 BF -8 BALL PISTON I-IYDROSTATICMACHINES This invention relates to ball piston hydrostatic machineswhich operate at high hydrostatic pressures, and this application is acontinuation of US. Ser. No. 71 1,966, filed Mar. 1 l, 1968 and nowabandoned, which was in turn, a continuationin-part of US. Ser. No.479,192 filed Aug. 12, 1965; US. Ser. No. 567,549 and US. Ser. No.567,623, now abandoned, both filed Jul. 25, 1966, all now abandoned.

Such machines may be either motors or pumps, and the torque output of amotor or input of a pump, for substantially constant line pressure,usually varies over each complete revolution. This is not alwaysdesirable, especially in a servomotor system.

An hydrostatic machine is one in which the mechanical output (motor) ormechanical input (pump) is a function of the pressure or potentialenergy of the working fluid rather than its velocity or kinetic energy.

The present invention is concerned only with an hydrostatic machine inwhich more than one ball is in contact with any one complete cam lobe.The latter is defined as that part of the cam lying betweencorresponding points on its profile. Points on the profile are said tocorrespond if the slopes of the profile thereat are equal in bothmagnitude and sign relative to a common datum. In a linear machine, thedatum is a straight line tangential to all the crests, or a lineparallel thereto. In a rotary or segmental machine, the datum is an arcof a circle tangential to all the crests, or an are described about thesame center. Thus, a cam lobe is that part of the cam profile lyingbetween adjacent crests or between adjacent troughs, or betweenalternate points of intersection with intermediate parts of the profileby a line parallel to, or described about the same center as, a linetangential to the crests.

In a linear or a segmental machine according to the present invention,therefore, this means that there are always fewer complete cam lobeslying between the points of contact of the first and last balls with thecam than the number of balls multiplied by the ball pitch. In a rotarymachine, according to the present invention, there are always more ballsthan complete cam lobes. For convenience of terminology, thisrelationship between ball pistons and cam lobes will be expressed as aratio of ball pitch to cam pitch of less than unity which will beassumed to apply throughout the subsequent description and claims.

In the graphical analyses which appear later in this specification,certain profiles or profile modifications have been drawn in anexaggerated fashion for clarity of illustration.

lt is an object of the present invention to provide a ball pistonhydrostatic machine having a ball pitch to cam pitch ratio of less thanunity in which the mechanical power output (motor) or input (pump) isconstant over each working cycle of the machine. For a rotary machine, aworking cycle is a revolution of its shaft. For a linear or a segmentalmachine, a working cycle is the relative displacement of the cylinderblock and the cam track equal to the ball pitch multiplied by the numberof balls.

To this end, it can be shown that if the cam track over which each ballmoves during each complete outward or inward stroke is profiled so as toproduce a ball motion having consecutive periods first of constantacceleration; then of constant velocity; and finally of constantdeceleration; and provided that the numbers of balls and of cam lobes ischosen so that the variation in thrust contributed by one ball during aperiod of acceleration or deceleration of that ball is compensated by anoppositely varying thrust contributed by another ball during acomplementary period of its stroke, or by the sum of appropriate partsof such thrust contributions by a plurality of other balls, then thetotal effect on the cylinder block will be one of constant thrust. (Forconvenience of subsequent description herein, the machines will beassumed to be rotary- -i.e. thrust torque). Thus, a rising torqueproduced by one ball of a rotary machine during an acceleration periodmust be complemented by a falling torque produced by at least one otherball during a coextensive deceleration period, these two torques addingup, at any given instant, to the same value of torque at any instantduring each complete cycle of the machine. Furthermore, it can bedemonstrated that the period of constant ball velocity relative to itscylinder reduces to vanishing point for certain combinations of numbersof balls and cam lobes, or can, for certain such combinations, be ofalternative determinate periods one of which, in special cases, is zero.(It should be noted that the velocity of, the rate of fluid displacementby, and the thrust produced by a ball are directly proportional to oneanother). This arrangement has the advantage of ensuring substantiallyconstant rate of flow of working fluid in the high pressure line andports, which promotes smooth running of the machine.

The generalized expression for the proportion of each stroke of a ballwhich is occupied by the component of constant velocity must not be lessthan the value of the expression 1 21 (x)/n where: n the number ofballs;

l= the highest common factor of n and the number (m) of cam lobes; and

x an integer which must be even when n /I is even. and must not exceed11 /2l.

Where a dwell is provided at the dead center regions of the cam profile,as hereinafter explained, the extent of the dwell is added to the periodof constant velocity given by the above expression.

For a six lobe, nine ball machine where no dead center dwell isprovided, therefore (I 3, n/l is odd) the period of constant velocity ofeach ball on each half lobe of the cam track is one third of the strokeof the ball. In this case, x cannot exceed unity because nl2l= 9/6 1.5.

Transient fluid pressures and thrust have been observed when thehydraulic circuit connections to a cylinder are reversed from high tolow pressure or vice versa at the ports in the pintle. To combat thesetransients a ball piston hydrostatic machine according to a feature ofthe present invention has its cam track profile modified in such a wayas to produce a dwell period during which each ball is stationary in itscylinder between successive port eventsi.e. during which a cylinder isnot connected to either an inlet or an outlet port in the pintle. Therelative positions and dimensions of the lands on the pintle are not socritical when the cam profile is modified as described to give the dwellperiods. In other words, the tolerances to which the pintle ports andcylinder ports must be machined are increased.

The insertion of a dwell in this manner changes the timing of thecommencement of the acceleration phase of the stroke and the end of thedeceleration phase of the stroke. For constant torque these timings inrespect of one ball are required to coincide respectively with the endand the beginning of the constant velocity phase of the stroke ofanother ball and the latter therefore require to be correspondinglyretimed. It thus becomes necessary to extend the constant velocity phaseas given by the said expression 1 21 (x)/n by the addition thereto of aperiod equal to the dwell period.

The cases where (in the absence of a dead center dwell period), theconstant velocity period reduces to zero, or where alternative lengthsfor the constant velocity period include an alternative where theconstant velocity period is zero, are those cases where l 2I(x)/n 0, andare confined to cases where n/l is an even number, (where 1: cannot beless than 2), and n/m is greater than 2.

The limitation previously stated that x must not exceed 11/21 is theequivalent of a limitation that the term 2i(x)/n must not exceed unity,for if it did, the length of the constant velocity phase would be aminus quantity, which is an absurdity. The cases where there arealternative values for the length of the constant velocity phase arethose where x can have a plurality of values without the-term 2l(x)/nexceeding unity. Itcan be shown that the term 2l(x)/n can never actuallyequal unity (to give a zero constant velocity phase) when n/l is an oddnumber because the numerator 21(x) is inevitably an even number and thedenominator n must be an odd number if n/l is odd; therefore thenumerator and denominator of 2I(x)/n can never be equal to one anotherto give the term a value of unity.

Where n/I is even 2l(x)/n may be equal to unity for some value of x,bearing in mind that x must be an even number. Some combinations of ballto lobe number. for instance 12 balls/ lobes, permit of more than onevalue for x which does not exceed n/Zl and some of these combinationsgive a value of unity for the term 21(.t)/n for the highest permissiblevalue of x.

Other n/I= even combinations, for instance 8 balls/2 lobes, have onlyone permissible value for x, namely 2, and 2l(x)/n can only equal unity.

Where there is a choice of more than one value for the length of theconstant velocity phase it is generally advantageous to choose theshortest as this choice provides the lowest acceleration anddeceleration at the region of the cam lobe crest where I-Iertzianstresses are highest due to the mutual convexity of the interacting balland cam surfaces in this region.

Another desirable characteristic of a ball piston rotary machine is thatthere should at all times be radial balance of the working thrust forcesacting on the balls. The requirement for radial balance is met if thereis a symmetry in the arrangement of balls relative to the entire camtrack. This condition of symmetry is satisfied if the number (m) of camlobes and the number (n) of ball pistons have a highest common factorFIG. 4 is a diagram similar to FIG. 3 where n/l is even;

FIG. 5 shows part of a single lobe cam diagram relating the velocity vof a single ball in a cylinder to the angular position 9 of the cylinderrelative to the pintle and showing a profile modification introduced bythe present invention to provide a stationary or dwell period for theball in the vicinity of inner dead center;

FIG. 6 is a schematic view ofthe profile of the cam track on either sideof the inner dead center position ofa ball showing the profilemodification necessary to produce the curve of FIG. 5;

FIG. 7 is a velocity/stroke diagram similar to FIG. I for a six ball onelobe cam machine showing modifications to provide dwell periods at thedead center positions of the balls; and

FIGS. 8A8D illustrate cam track modifications at the sections A-A to D-Din FIG. 1.

(For convenience, the remaining FIGS. 9-14 of the accompanying drawingsare described hereinafter).

Referring first to FIGS. 14, each abscissa represents strokes of a ballpiston and each ordinate represents ball piston velocity. In FIGS. 1 and2, each horizontal row of triangles represents, in the simplest form,the basic essentials of a stroke-that the ball must accelerate from restat one dead which is an integer greater than unity. Thus, for example,if center locanon on the cam to a certain peak velocity and the numberof lobes m is equal to 6 and the number of balls n is equal to 9, thehighest common factor is 3, so that there are always balls spaced at 120around the shaft axis, each ball being at the same position of itsstroke as its other two counterparts on an equivalent segment of thetrack.

The balls in a machine according to the present invention may bearranged either internally or externally of the cam track, and eitherthe cylinder block or the track may be arranged to rotate within a fixedhousing. For a servomotor application of the invention, however, themachine must have maximum stiffness, defined in terms of possiblepositive and negative limits of displacement error of the follower motorrelative to the desired position signalled by the input. Hence, for thisapplication of the invention, the volume of oil trapped in the machinebetween the balls and the servocontrol valve must be a minimum.

Where it is necessary to achieve radial balance of the thrust forces,the number of lobes and the number of balls are both restricted by theneed for geometrical symmetry in the relative dispositions of the ballsand the lobes. Taking, for example, the case ofa nine ball machine witha six lobe cam, the following equations define the shape of eachhalf-lobe.

9 2 o 0 for 20 $0330 where r, radial distance from machine axis tocenter ofa ball at inner dead center on the cam track, r =radialdistance from machine axis to center of a ball at outer dead center onthe cam track,

r= instantaneous radial distance from machine axis to ball center at anygiven position of the cylinder block in relation to the cam track.

A graphical analysis of the behavior of the ball pistons ofa machineaccording to the present invention will now be given with reference toFIGS. l-7 of the accompanying drawings in which:

FIG. 1 is a diagram for a nine ball, six lobe machine;

FIG. 2 is a diagram for a nine ball one lobe machine; the left-hand andright-hand halves of this FIG. showing alternative choices for thelength of period of constant velocity;

FIG. 3 is a single triangle taken from a complete velocity/strokediagram ofa machine in which the ratio n/l is odd, and illustrating fouralternative choices for the length of period of constant velocity;

decelerate from that peak velocity to rest again at the opposite deadcenter location on the cam.

In FIG. 1, each line of triangles is numbered (1 to 9) to represent arespective ball of a nine ball six lobe machine,

0 each triangle pertaining to a respective cam half-lobe. All the linesare of equal length representing the complete cam track pitch or 360 ofcam track, and each line is divided into 12 equal intervals, eachrepresenting one half cam lobe, or one full stroke of the respectiveball. These subdivisions of successive lines are mutually displacedhorizontally (to the left in the drawing) by one-ninth of the completeline length (representing 360 as aforesaid), to represent the relativeangular displacements of successive balls, the timed events proceedingfrom left to right and the balls being numbered in the order in whichthe balls pass a given point on the cam track.

The triangles in each line are drawn alternately positive (above theline) and negative (below the line) to represent, respectively,alternate high and low pressure strokes of the ball concerned. For amotor having a rotary cylinder block enclosed by a fixed annular camtrack, a working stroke is outwards with respect to the shaft of themachine; for a similarly arranged pump, a working stroke is inwards.Every fourth line of triangles is geometrically identical. 7 I

""Eachconiplete triangle represents a basic condition of motion of theball comprising a half stroke at constant acceleration followed by ahalf stroke at constant deceleration. A period of constant velocity isrepresented by cutting off the peak of each triangle parallel with itsbase. It becomes neces- 3) 55 sary to do this to achieve constant torqueexcept in circumstances where the apex of a triangle for one ballcoincides in time with the zero crossing point of the triangle foranother (conjugate) ball so that each rising triangle side for one ballis coterminous with the falling side ofa stroke triangle for a conjugateball (comparing power stroke with power stroke and induction/exhaust oridle stroke with induction/exhaust stroke). Subject to an exceptiondescribed below in relation to FIG. 2, the criteria for determining thelevel at which the peak of a triangle is to be cut off to provide theappropriate constant velocityphaseare: a. that the start of eachconstant velocity period (i.e. the finish of a period of constantacceleration) of each ball must coincide with the finish of a period ofconstant deceleration ofa conjugate b. the end of the constant velocityperiod of one ball must coincide with the beginning of the constantacceleration o f a conjugateball. These criteria are satisfied inFIG. 1. For example, taking ball No. 1, let the top left trapezium 1Arepresent a working stroke of the ball No. l and the adjacent trapezium1B represent an idle stroke thereof. Then the left flank of thetrapezium 1A coincides in time with the right flank of the firsttrapezium 3A (only partly shown) of ball No. 3. Similarly, the rightflank of the first trapezium IA coincides with the left flank of thefirst trapezium 2A of ball No. 2. Thus. the constant velocity period ofthe trapezium 1A of ball No. 1 starts at the same instant as the firstintersection 3x of the velocity/stroke curve for ball No. 3 with thezero or base line for that ball, and finishes at the first intersection21: of the velocity/stroke curve of ball No. 2 with its zero or baseline. To indicate this, the starts and finishes of the constant velocityperiods of the trapezia 1A, 1C and 1D for ball No. 1 are marked by thebracketed numerals (3) and (2) respectively, which identify thecomplementary curve which establishes the relevant point on the curve ofball No. 1. Similar identifications appear on other ball curves.

In the particular configuration of machine to which FIG. 1 relates, itso happens that there are more than one set of complementary conditionsto establish the duration of each constant velocity period. Balls Nos.1, 2 and 3 form one complementary group, complete in itself, whilstballs Nos. 4, 5 and 6, and balls Nos. 7, 8 and 9 likewise formcomplementary groups each complete in itself. This arises from therelatively large value ofl (=3) whereby the stroke diagrams,successively displaced by the ball pitch, come into phase again everyfourth ball.

Although only positive trapezia have been specifically considered in theforegoing analysis, it will be evident by the symmetry of the systemthat the constant velocity periods of 'negative trapezia for any oneball can be similarly established in relation to the curves of conjugateballs.

A simple method for constructing diagrams of this type, for differentcombinations of ball number and lobe number, is to choose a convenientlength for dividing up into basic triangle stroke diagrams correspondingto the number of lobes and to construct separate stroke diagrams for therespective balls, one below another and each displaced laterally fromthe one above it by a distance equal to the said length divided by theball number.

Vertical lines are then drawn, from top to bottom of the diagram,through every point where a stroke triangle for a ball intersects thezero line. A number of such vertical lines are shown at the right handside of FIG. 1.

It will be found that these lines are separated by a distance being aproportion of the length of a stroke which is equal to [M where 11/! isodd and 2l/n where 11/! is even. In a limited number of the latter casesthese vertical lines will pass through the apices of stroke trianglesand these are the cases where constant torque can be obtained with aconstant velocity period of zero. In all other cases it will be foundthat the apex of each stroke triangle is flanked by at least one pair ofsuch vertical lines which intersect the sides of the triangle, the linesof a pair being equidistant from the apex. The points of intersection ofthe lines of any such pair with the sides of the triangle mark thebeginning and end of the constant velocity period which, when insertedinto the middle of the stroke, will provide the required constant torquecharacteristic.

FIG. 2 shows a graphical analysis, generally similar to FIG. 1, of ballvelocities in a nine ball, one lobe machine, but for this ball/lobecombination, several pairs of vertical lines symmetrically flank theapex of each triangle, so that alternative periods of constant velocityare obtainable for each curve. Obviously, only one alternative will beembodied in any one machine. In FIG. 2, the longer alternative constantvelocity period is illustrated in the left hand half of the FIG. and theshorter alternative period is illustrated in the right hand half.

For this particular configuration of machine, it so happens that thereare in fact four alternative periods of constant velocity, the twoactually drawn being the shortest (right hand side) aridthe longest butone (left hand side). The limits of these are indicated, on the curve 5Afor ball No. 5, by the pair of bracketed numerals (3) and (7) and, onthe curve 1A for ball No. l, by the pair of bracketed numerals (9) and(2). Verticals drawn through each of these points pass through theintersections of the other identified ball curves with their respectivezero lines when the said other curves are parallel to the flanks of thecurve 1A or 5A. This condition is the exception to the criteria (a) and(17) previously referred to in connection with FIG. 1, but is justifiedas follows:

Taking, for purposes of illustration the curve 5A. each flank of thetrapezium between its point of intersection with the zero line and thecorresponding end of the constant velocity line at (3) or (7),respectively. can be subdivided into four parts of equal length markedby arrowheads. Each lowermost subdivision is now seen to be exactlycomplementary to the corresponding subdivision of an oppositely inclinedflank of a curve of a conjugate ball, that on the left flank of thecurve 5A being complemented by the lowermost subdivision of the curvefor ball No. 9 and being marked 9, whilst that on the right flank iscomplemented by the curve for ball No. 2. and is marked 2. Thecomplementary subdivisions are connected by dotted lines.

Similar complementary pairs for-the curve 5A are also connected bydotted lines and marked with the appropriate numerals. Correspondingmarkings are shown on the curves 4A and 6A, and symmetry shows that thesame analysis can be made for all the ball velocity/stroke curves in thediagram. Consequently, this arrangement of machine provides constanttorque.

In a 9/1 machine (FIG. 2), nl] is odd, so that the duration of aconstant velocity period is l 2l(x)/n. It can be shown that for the lefthand side of FIG. 2, x 2, and for the right hand side x=4.

The other two alternative periods of constant velocity in FIG. 2 obeythe criteria (a) and (b) mentioned above in connection with FIG. 1, andthe value of x is 3 for the shortest but one, and l for the longest.

FIGS. 3 and 4 show the comparison between two similar trapezia,representing ball velocity/stroke curves, for machines where n/l is oddand even, respectively. The two FIGS. illustrate alternative lengths ofthe constant velocity period.

In a motor, the useful output is a mechanical force linear thrust for alinear machine and rotary torque for a rotary or oscillatory segmentalmachine. In a pump, the useful output is an hydraulic pressure. Theforegoing analysis has concerned itself with the behavior of a ballpiston, but it will be appreciated that displacement of a ball isexactly proportional to displacement of a volume of hydraulic fluid(ignoring, as is justified in all normal working applications of theinvention, compressibility of the fluid). Hence, the ordinates of any ofthe curves of FIGS. l4 can be expressed in terms of volum of fluiddisplaced on each stroke of a ball piston.

A factor making it desirable to modify the ball stroke/velocitycharacteristics represented by FIGS. 1 to 4 is that a practical machinewill always require a finite period of time for reversal of portconnections to the cylinders. In a rotary machine, these are customarilycontrolled by a pintle valve in the cylinder block, and although therate of displacement of a ball in its cylinder is a minimum at the timeof reversal of the port connections, and although also there willinevitably be leakage of fluid between relatively moving componentswhich will tend to reduce back pressures, it is nevertheless ofadvantage to be able to give a ball piston zero displacement over theperiod of port reversal.

FIGS. 5 and 6 illustrate the conditions which obtain if a dwell periodis provided at the crest of a cam lobe. The point I represents thenormal point of intersection of the zero line by a flank of avelocity/stroke trapezium, but when the ball is required to remainstationary in its cylinder for a brief period, its velocity falls tozero along the curve 22 before it reaches the point I and begins toincrease from zero along the curve 20 from a point beyond it. Theintervening dwell period is represented by the distance I. During thisperiod the ball travels over the flattened crest 23a (FIG. 6) of the camlobe 23. In these circumstances, each period of constant velocity mustbe extended at each end by an amount at least equal to one half thedwell period I on a complementary curve so as to ensure that it will bepossible for the dwell period of any one ball to be "covered" by aconjugate ball in contact with a constant velocity segment of the camtrack.

This is illustrated in FIG. 7. which is a diagram similar to FIG. 1 butrelating to a six ball. single lobe cam machine. In this FIG., thevelocity/stroke curves for balls Nos. 1-5 are shown in full lines forobtaining a constant torque characteristic without a dwell period. asexplained with reference to FIGS. 1-4. The curve for ball No. 6 is shownpartly dotted to indicate the profile modification necessary tointroduce a chosen short dwell at each dead center position, theduration of this dwell being determined by the minimum requirements forsmooth port connection reversal for each cylinder. The same form ofnotation is used in FIG. 7 to indicate complementary ball conditionsdetermining the limits of the constant velocity periods as is used inFIGS. 1 and 2, except that the extended limits of such periods tocomplement part of a dwell period of another ball are marked by anumeral with a supplementary dash (e.g. 6 on curve 2) and the limits ofa dwell period are marked by numerals with two supplementary dashes(e.g. 2" on curve 4). In all cases, the numeral itself identifies thecomplementary curve. For illustration purposes, dwell periods areindicated on even numbered curves only, and only their positions, andthe positions of the limits of extension of the constant velocityperiods are shown on curves 2 ar d 4 for simplicity of drawing, it beingunderstood that the profile modifications illustrated on curve 6 will berepeated on all the other curves when dwell periods are incorporated.

Referring to specific instances of dwells and constant velocity periodextensions as shown in FIG. 7, it will first be noted that the zerointersections of the basic curve of ball No. 6 determine the finishpoints of the constant velocity periods of balls Nos. 2 and 4 (assumingthat the displacements of the cylinders relative to the cam track are inthe direction of the arrow R). Hence the limit point (6) of eachconstant velocity period of ball No. 2 is extended to (6) to complementthe second half of the dwell period of ball No. 6 which terminates at(2"). The first half of this dwell period which begins at (4") iscomplemented by the advance of the start of the constant velocity periodof the negative-going trapezium of ball No. 4 from the point (6) to thepoint (6"). Similarly each dwell period of each other ball iscomplemented by extensions of the constant velocity periods of two otherballs. Since each dwell period of a ball represents a power loss in themachine, the periods of dwell are kept to the minimum consistent withsmooth reversal of cylinder port connections.

Due to high mutual convexity of the ball and the cam track in theregions of the crests of the lobes, high Hertzian stresses are apt tooccur, accelerating surface fatigue failure at thesev points. Thesestresses may be mitigated by local modifications of the grooving of thecam track adjacent the inner dead center position. These modificationsare illustrated diagrammatically in FIGS. 8A-8D. The lines A-A, B-B, C-Cand D-D on the curve of ball No. 9 in FIG. 1 mark successive pointsalong the cam track at which the groove is as shown in the correspondingFIGS. 8A, 8B, 8C, and 8D. At the section A-A of FIG. 1, the groove isshallow as shown at a in FIG. 7A. At the section B-B, the groove isdeeper, as indicated at 15b in FIG. 88, whilst at the section C-C it isdeeper still, as illustrated at 15c in FIG. 8C. Maximum depth is reachedat D-D, as indicated at 15d in FIG. 8D, which represents the transversecross section of the crest of the cam track 14 at the inner dead centerposition. The radius of the groove is slightly greater than that of theballsay, 1.025 x rwhere r is the ball radius.

Practical embodiments of the invention are illustrated, by way ofexample, in the remaining FIGS. of the accompanying drawings in whichg gH 7 FIG. 9 is a simplified velocity/stroke diagram of a pump or motorhaving nine balls and eight lobes, the ordinates being calibrated interms of oil displacement per unit of time (or angle an d the abscissaein time (or angle) ofrotation;

' FIG. 10 is a transverse cross section ofa machine operating on theprinciple of FIG. 9;

FIG. 11 is a longitudinal cross section through the machine of FIG. 10;

FIG. 12 is a section similar to FIG. 10 ofa nine ball, six lobe machineas analyzed in FIG. 1;

FIG. 13 is a diagrammatic section similar to FIG. 10 of a 16 ball, fourlobe machine; and

FIG. 14 is a velocity/stroke diagram for the machine of FIG. 13.

Referring first to FIG. 9, the machine represented has nine ball pistonsand eight cam lobes. Assuming that the machine is a pump driven atconstant speed; that the zero position of the shaft coincides with thecommencement of a period of constant acceleration of ball No. I on aworking stroke. and that the pump delivers against a constant highpressure, the curve of volumetric output per second (or per degree ofrotation) provided by ball No. l is the trapezium marked 1 at the originof the coordinate axes. Output first rises linearly with time or angle,during the period (2 of constant piston acceleration. When this changesto constant velocity, the output remains constant, and when this in turnchanges to constant deceleration the output falls linearly.

Since the cam track has eight lobes, each lobe subtends 45 at the axis,and each stroke of a ball, whether working or idle, subtends an angle of22 /2. Hence the base of the trapezium is 22 /2, and successive trapeziafor the same ball are spaced by 22 /2.

While the first ball is executing its period of constant velocity on itsworking stroke, ball No. 2 begins its period of acceleration on itsworking stroke. This is shown in the trapezium numbered 2 commencing ata shaft angle of 5. It spans the range of shaft angles 5 to 27 /5 -i.e.22 /5 as before-and it will be noted that the curve of rising output forthe period of uniform acceleration of ball No. 2 is exactly coextensivewith, and of equal but opposite slope to, that of uniform decelerationof conjugate ball No. 7. This balance of outputs occurs at each 5interval of shaft rotation, the period of deceleration of ball No. 1coinciding with the period of acceleration of conjugate ball No. 5.Hence, the total output is a constant. Since the output pressure isassumed to remain constant, the values of the ordinate also representtorque output in the case ofa motor, and this torque thus remainsconstant.

FIGS. 10 and 11 show a practical construction of machine operating inaccordance with FIG. 9 and having the locus of its ball centers derivedfrom the velocity curves of FIG. 9. The cam profile shown in FIG. 10 isdiagrammatic since it is not possible to indicate, in a drawing on thisscale, the details of shape as rigorously derived so as to reproduce theball motions defined by FIG. 9. The rigorous cam profile is the envelopeof a series of circles, having the same radius as the balls, whosecenters lie on a ball center locus derived from FIG. 9. The cam trackmay be machined by a substantially spherical cutter, of radius equal tothe ball radius, whose rotational axis is constrained to follow thelocus of the ball center.

The machine is basically a conventional ball piston machine having arotary cylinder block 40 carrying ball pistons l-9 in radial cylinders41-49. The balls run on an eight-lobe cam track 50 formed on theinternal circumference of a cam ring 51. The cylinder block 10 runs inantifriction bearings 52, 53 in a rigid housing 54, and a pintle 55 issupported at its outer end in a stepped bore 56, 57 in a port block 58secured to the housing, and at its inner end in needle bearings 59 inthe cylinder block 40. The pintle 55 has the usual system of inlet andexhaust ports 60, 61 which register successively with each cylinder41-49 in turn, and are connected to the external hydraulic circuit 62through respective longitudinal ducts 63, 64.

The positions of r,, and r are marked for one lobe in FIG. 10.

FIG. 12 illustrates the arrangement ofa ball piston machine whichfulfills the condition of operation represented in FIG. 1, and exhibitsradial balance of forces on the pintle and cam track. The balls 1, 2,3-work in respective cylinders 41, 42, 43-angularly spaced at 40 arounda cylinder block 40. The balls run on a six lobe cam track 50 formed ona cam ring 51,

each half-lobe being divided into three segments defined by the limitsof angle for equations 1 )(3) above, and its profile being derived fromthe locus of the ball center as described with reference to FIGS. and11. The positions of r,, and r for one half-lobe are shown in FIG. 12.The construction of this machine is otherwise similar to that shown inFIGS. 10 and 11.

In both the foregoing machines, the cam track must be accuratelymachined. The balls l 9 must also be accurately ground and a goodsealing fit in their respective cylinders 41 49. There is no fixedrelationship between ball diameter and cam profile, constancy of thetorque being maintained.

Since a machine of the general layout of FIGS. 10 and 11 or FIG. 12 canbe designed to have a minimum value of trapped oil between the balls 1-9and the servocontrol valve (not shown), the invention is particularlysuitable for servomotor systems. In a machine as shown in FIG. 12constructed in accordance with the present invention, the followingoperating data were recorded:

Displacement 22 in lrev Hydraulic Stiffness 590,000 lb. in/rad. NaturalFrequency 230 c/s. Maximum Pressure 2000 lb./in Torque per lb./in 3.5.lb. in.

Overall Dimensions Weight 45 lb.

FIG. 13 is a diagram of a four lobe cam in a 16-piston machine. The camtrack is represented at 35, and the axes of the ball pistons at 36.

FIG. 14 shows a ball stroke/velocity diagram for this machine. In theexpression 1 21x/n, x can have only the value 2, since I 4 and n/2I,which represents the maximum permissible value of x, is equal to 2. Themachine has four complete groups of conjugate balls in each of which therelative position of each ball on a cam lobe exactly corresponds withthat of a counterpart ball of each other group on its respective camlobe. In FIG. 14, the curves for the group of balls Nos. 13-16 are shownwith a dwell extending over 4, at each inner dead center, and this isbalanced by a constant velocity period of the same duration.

In the preceding description of the invention reference has been made tomachines in which the pistons consist of balls. Variants are possible inwhich each ball is backed by a cylindrical piston element the form ofwhich can vary between a sealing ring to reduce the leakage of a ballpiston and a cylindrical piston in which the role of the ball is that ofa mere cam follower; in the case of the latter the diameter of the ballcan be less than the diameter of the cylindrical piston element, or theball may be replaced by a cam follower wheel journaled in a bifurcatedend of the cylindrical piston element.

Machines of this modified construction are subject to the same rules forobtaining constant torque and are within the scope of the invention.

We claim:

1. A cam controlled reciprocating piston hydrostatic machine having apiston pitch/cam pitch ratio less than unity and constant mechanicalthrust characteristics throughout every cycle of operation, comprising acylinder block forming a housing for a plurality n of cylinders carryingpistons movable on a cam track having a plurality 2m of similarlycontoured half-lobes each having a profile which determines, for eachpiston moving thereover, a stroke having consecutive periods of constantacceleration, constant velocity and constant deceleration, thevariations in thrust of any one piston during said acceleration anddeceleration periods being compensated by respective oppositely varyingthrusts resulting from the simultaneous movement of at least one otherpiston over the appropriate segment of the cam track, and the proportionof the stroke occupied by the constant velocity period (excluding anyextension to cover a dwell period at inner d eacl 8%" Dia. 9" long.

center of each piston) being given by the expression I 2l.r/n. where Iis the highest common factor of m and n; and .t is an integer which mustbe an even number whenever the value n/! is even. and whose magnitude isnot greater than 11/21. x being chosen within the following limitations:

i. x must be a positive integer;

ii. x must be even when n/! is even:

iii. x must not exceed the value of 11/21 and m and n being chosen sothat the value of the expression ZIx/n does not exceed unity for thesmallest permissible value for x.

2. A machine according to claim I having radial balance, at any positionof the cylinder block relative to the pintle, of the working thrustforces acting on the piston, wherein the cylinders are radially disposedin a rotary cylinder block, and all of the pistons which at any giveninstant are at the same positions in their respective strokes aregrouped symmetrically about the shaft axis, each piston being at thesame point on its coacting cam lobe as each other ball in the samesymmetrical group.

3. A machine according to claim 1 wherein the profile of each half-lobeof the cam produces a piston stroke having consecutive ideal periods ofconstant acceleration and constant deceleration, and the thrustvariations during said acceleration and deceleration periods arecompensated by respective oppositely varying thrusts resulting from themovement of at least one other piston over the appropriate segment ofthe cam track, the value of x in the expression 1- 2Ix/n being such thatthe expression reduces to zero.

4. A machine according to claim 1 wherein the cross-sectional shape ofthe cam track is modified locally at points of change of acceleration toreduce l-lertzian stresses in the cam track.

5. A machine according to claim 4 wherein said pistons comprise pistonsof circular profile in cross section, the cam track is groovedtransversely of its length at a radius about 2 /2 percent in excess ofthe radius of the pistons, and the depth of the groove progressivelyincreases from either side up to the crest of each lobe at the innerdead center position of a piston.

6. A machine according to claim 1 wherein the rigorously derived camprofile is modified at each junction between consecutive periods ofdeceleration in one sense and acceleration in the opposite sense toprovide a short dwell period in which the velocity of a piston axiallyof its cylinder is substantially zero, the said dwell period being of aduration sufficient only to permit the cylinder port connections to bereversed, and each rigorously derived period of constant velocity of apiston being extended at each end to compensate for a corresponding halfof a dwell period of another piston.

7. A machine according to claim 1 wherein said pistons comprise pistonsof circular profile in cross section and wherein the cam has six lobesand the cylinder block has nine pistons, and the profile of eachhalf-lobe of the cam is such that each stroke of each piston conforms tothe equations:

where 0 the angle subtended at the axis of the machine by the locus of apiston center from its dead center position up to its instantaneousposition; where r radial distance from machine axis to center of apiston at inner dead center on the cam track; r radial distance frommachine axis to center of a piston at outer dead center on the camtrack; r instantaneous radial distance from machine axis to pistoncenter at any given position of the cylinder block in relation to thecam track.

1. A cam controlled reciprocating piston hydrostatic machine having apisTon pitch/cam pitch ratio less than unity and constant mechanicalthrust characteristics throughout every cycle of operation, comprising acylinder block forming a housing for a plurality n of cylinders carryingpistons movable on a cam track having a plurality 2m of similarlycontoured half-lobes each having a profile which determines, for eachpiston moving thereover, a stroke having consecutive periods of constantacceleration, constant velocity and constant deceleration, thevariations in thrust of any one piston during said acceleration anddeceleration periods being compensated by respective oppositely varyingthrusts resulting from the simultaneous movement of at least one otherpiston over the appropriate segment of the cam track, and the proportionof the stroke occupied by the constant velocity period (excluding anyextension to cover a dwell period at inner dead center of each piston)being given by the expression l - 2lx/n, where l is the highest commonfactor of m and n; and x is an integer which must be an even numberwhenever the value n/l is even, and whose magnitude is not greater thann/2l, x being chosen within the following limitations: i. x must be apositive integer; ii. x must be even when n is even; iii. x must notexceed the value of 21 and m and n being chosen so that the value of theexpression 21x does not exceed unity for the smallest permissible valuefor x.
 2. A machine according to claim 1 having radial balance, at anyposition of the cylinder block relative to the pintle, of the workingthrust forces acting on the piston, wherein the cylinders are radiallydisposed in a rotary cylinder block, and all of the pistons which at anygiven instant are at the same positions in their respective strokes aregrouped symmetrically about the shaft axis, each piston being at thesame point on its coacting cam lobe as each other ball in the samesymmetrical group.
 3. A machine according to claim 1 wherein the profileof each half-lobe of the cam produces a piston stroke having consecutiveideal periods of constant acceleration and constant deceleration, andthe thrust variations during said acceleration and deceleration periodsare compensated by respective oppositely varying thrusts resulting fromthe movement of at least one other piston over the appropriate segmentof the cam track, the value of x in the expression l - 2lx/n being suchthat the expression reduces to zero.
 4. A machine according to claim 1wherein the cross-sectional shape of the cam track is modified locallyat points of change of acceleration to reduce Hertzian stresses in thecam track.
 5. A machine according to claim 4 wherein said pistonscomprise pistons of circular profile in cross section, the cam track isgrooved transversely of its length at a radius about 2 1/2 percent inexcess of the radius of the pistons, and the depth of the grooveprogressively increases from either side up to the crest of each lobe atthe inner dead center position of a piston.
 6. A machine according toclaim 1 wherein the rigorously derived cam profile is modified at eachjunction between consecutive periods of deceleration in one sense andacceleration in the opposite sense to provide a short dwell period inwhich the velocity of a piston axially of its cylinder is substantiallyzero, the said dwell period being of a duration sufficient only topermit the cylinder port connections to be reversed, and each rigorouslyderived period of constant velocity of a piston being extended at eachend to compensate for a corresponding half of a dwell period of anotherpiston.
 7. A machine according to claim 1 wherein said pistons comprisepistons of circular profile in cross section and wherein the cam has sixlobes and the cylinder block has nine pistons, and the profile of eachhalf-lobe of the cam is such that each Stroke of each piston conforms tothe equations: